1
Expert Design and Empirical Test Strategies for Practical Transformer
Development
Victor W. QuinnDirector of Engineering / CTO
RAF Tabtronics LLC
2
• Units• Design Considerations• Coil Loss• Magnetic Material Fundamentals• Optimal Turns• Empirical Shorted Load Test • Core Loss Estimation and Recommended
Empirical Test Method (iGSE,FHD,SED)• Example Application• Summary
Outline
Victor [email protected] Ext 340
3
• Transformer developers strive to design, develop and consistently manufacture transformers based on in depth understanding of application conditions and implementation of best practice design, production and test methods.
• The initial first article transformer must be carefully validated in the respective application circuit to ensure the scope of thecomponent development was sufficient for the end use.
• Based on the challenges of accurate measurement of transformers in complex circuit applications, calorimetric (temperature rise) measurements are often used to characterize transformer power dissipation levels.
• The transformer developer may work closely with the power system developer to correlate loss and thermal measurements under specific conditions.
• Once the transformer design is validated, the transformer developer must implement tight QA controls on component materials and processes to ensure consistent results.
New Product Development PremiseComponent Verification Application Validation
4
Electric Field
VoltMeter
BWebersMeter
WeberMeter
Tesla Gauss
HAmpere Turn
MeterATM
Oe
JAmpereMeter
Ohm MeterHenryMeter
HM
FaradMeter
ff
2 24
2
2
07 6
12
0
1 10
1 10
1 1
4 10 1257 10
885 10
1
1.257
(permeability constant)
(permittivity constant)
where = frequency in Hertz
0
.
.
,
UNITS: Rationalized MKS+
) 20 @ ( 676.0 CelsiusCuinch
inchF12
0 10225.0
) 20 @ ( 6.2 CelsiusCuinchf
1 Oe = 2.02 AT/inch
inchAG
inchH 5.01019.3 8
0
5
Φ
IsIp
Design ConsiderationsCross Sections and Operating Densities
Primary Secondary
CoreCore cross section [Acore] constrained by aperture of coil.
Coil cross section [Awindow]constrained by aperture of core.
ΔB
J
ΔB
J
6
Faraday’s Law
• When a voltage E is applied to a winding of N Turns
E Nddt
( )
(Instantaneous Volt/Turn Equivalence)
E dt
N
pt
t T
p
1
1
2
ET
E dtt
t T
1
1
1
(Average Absolute Voltage)
Voltage
Time
E +
-
Np
E
Ns
7
Voltage
Time
v(t) +
-
i(t) L
v(t)
+
-
i(t)
L
Flux Density Considerations
• Voltage driven coil
• Line filter inductor
Current
Time
(Two induced consecutive, additive voltage pulses)
ENp
E dt
N
pt
t T
p
1
1
2
8
Ampere’s Law
• When a current i is applied to a winding of N Turns
• For ideal core having infinite permeability, Hc=0
(Instantaneous Amp-Turn Equivalence)
Ip
Np Ns
encloseddlCurve C
H i
Is
sspp ININ
Curve C
Hc
Is
Ip
The Amp-Turn imbalance is precisely the excitation required to achieve core flux density. Magnetic material reduces the excitation current for a given flux density.
9
Transformer VA Rating• Faraday’s Law and Ampere’s Law imply that
instantaneous Volt/Turn and Amp-Turn are constant.
• Therefore the winding Volt-Ampere product is independent of turns and is a useful parameter to rate transformers.
• Since core flux excursion is based upon average absolute winding voltageand winding dissipation is based upon RMS current , define:
iRMS
Transformer VA E iRating ii
RMSi
E
10
Fundamental Transformer Equation
• Derive a relationship between Volt-Ampere rating and transformer parameters:
• Therefore, by increasing frequency, current density, flux density, or utilization factors, the area product can be reduced and the transformer can be made smaller.
VA A A freq J B K KRating core window Fe Cu
VAP A AVA
freq J B K Kcore windowRating
Fe Cu
11
Current Density (J ),Window Utilization Factor (KCu )and Coil Loss
12
• At low frequencies, for uniform conductor resistivity and uniform mean lengths of turn, minimum winding loss is achieved when selected conductors yield uniform current density throughout the coil.
• For uniform current density J:
or
where
2 JVolCondLossCoilFrequencyLow 2
iiNILossCoilFrequencyLow
AreaWindowCoreKy
Thicknessxy
Cucu
Window Utilization Factor
Coil Loss
13
Coil Insulation Penalty
• Conductor Coatings• Insulation Between
Windings• Insulation Between
Layers• Margins• Core Coatings or
Bobbin / Tube SupportsThese considerations can total more than half of the available core window limiting utilization to less than 35%!
Core Window
Window Utilization Factor (KCu )
14
Example of KCu Estimate (PQ 20/20)
tol
supporttol
tol
margin
2IW2IW
Δx
Δz
318.0KKKK ,
556.00.169
2(0.01)-(0.035)0.0102169.0Δz
2(2IW)-(support)tol2ΔzK
85.0) (K
785.04
) (K
0.858 0.55
2(0.036)-2(0.003)-0.55 Δx
flange) bobbinor 2(margintol2ΔxK
zCuinsulCushapeCuxCu
zCu
insulCu
shapeCu
xCu
CuKSo
wiresolidfilmheavy
squareversusround
15
Window Utilization Penalties
Coil Loss
0
2
4
6
8
10
12
14
0 5 10 15 20
Frequency (kHz)
Loss
(W)
Window Utilization
0%10%20%30%40%50%60%70%80%90%
100%
0 5 10 15 20
Frequency (kHz)
Util
izat
ion
Ideal
Typical Core Window Utilization
0%
25%
50%
75%
100%
Insulation occupies more than 50% of core window.
Eddy current losses can further reduce effective conductor area by more than 50%.
16
Other Design Considerations AffectingWindow Utilization: KCu
MaximumKcu
LeakageInductance
CapacitanceNumber OfWindings
EddyCurrentLosses
InsulationRequirements
Corona / DWVRequirements
17
xRHxzH RMS ˆˆ)( 0
xHxzH RMS ˆˆ)( 0
yzJ ˆ)(
z
x
y
Low Frequency Example Calculation of Loss
z
Effective conductor thickness
zxiydyJzxLoss
zxi
zHR
zH
dzdHJ
xHiR
ixLawsAmpere
RMS
yy
RMSy
RMS
RMS
2
2RMS
RMS 0RMS
RMS 0
RMS 0
)1(
1
1)H-(R '
18
Qualitative ExampleSevere Skin / Proximity Effects
( ) cos( ) H H t x0
H t x0 cos( )
J H J H
H dl i H tilcurve w
0 0
1
2 2
,
cos( )
i
J0
J0
J J0
J
Circulating Current
z
zx
19
Dissipation And Energy As Function Of B (single layer)
0
0.5
1
1.5
2
2.5
0.5 1.5 2.5 3.5 4.50
0.5
1
1.5
2
2.5
DissipationDissipation Average Energy
Average Energy
x y Hs 02
8
Minimum Dissipation @ B=π/2
2SH
2 yx
H H Hs s s1 20 ,
Single layer with one surface field at zero is forgiving of design errors.However, other constructions can yield lower loss.
Bz
20
Loss Equivalent and Energy Equivalent Thicknesses (Single Layer Portion)
magnetic
loss
equivBB
BB
equiv
BB
BB
ThkBeeBee
ThkBeeBee
zwith B
2RMS
022
222
RMS0
2RMS
22
22
2RMS
SS2S1
)(NI x6y ]
)2cos(2)2sin(2[
23)(NI
x6y Energy
/)(NI xy
] )2cos(2)2sin(2[
)(NI xy Power
) HH and 0H(
21
Define Normalized Densitiesfor General Sine Wave Boundary Conditions
),B(R,pHPower 020RMS
yx
• Δx Δy represents the surface area of the conductor layer
• H0RMS=RMS value of sinusoidal magnetic field intensity at one boundary
• R=Ratio of magnetic surface field Intensities
• B=Ratio of conductor thickness to δ (conductor skin depth)
• Ф=Shift of magnetic surface field phases
),B(R,eH Energy Magnetic 020RMS0 yx
Dimensionless densities (p0 , e0)
22
Complex Winding CurrentsDissipation For Frequency Dependent Resistor
For complex waveshape and frequency dependent resistor, Harmonic Orthogonality =>
V IRP I R
P I Rdt
P RT
I dt
P R Irms
IrmsT
I dt
ave TT
aveT
ave
T
2
1 2
2
2
2
1
1
*
P R f Irmsave total n n n ( ) * 2
+ _V
I Power
23
Nonsinusoidal Excitation
• is the RMS current value at the kth harmonic
• is the RMS value of the complex waveshape
• is the ratio of the RMS value of the kth harmonic to the RMS value of the complex waveshape
rmsdc II 0rmsrms II 11
rmskrms IIk
.krmsI
rmsI
k
24
Nonsinusoidal Currents andMulti-Layer Winding Portion
Derive equivalent power density function
Where B1 is the ratio of conductor thickness to skin depth for the first harmonic
Sum results to derive equivalent winding thickness and effective window utilization
,0B iR,piB
RBRp 1iiequiv
02
1
22010 10,,
l
l
n
n1equiv
l1l
Cu
n
n1equiv
l
,0Bn
pnnBn
K
,0Bn
pnn
sn Thicknesing Portioalent WindLoss Equiv
10
2
10
2
,11
1
,11
25
Portion UtilizationSine Wave, No Insulation
Conductor Utilization In PortionNo Insulation
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
0.00 1.00 2.00 3.00 4.00 5.00 6.00Portion Thickness (in skin depths)
KCuz
For portions less than 3 skin depths thick, utilization increases with increasing layers.
12
34
56
7Layers
Sum of 10 Harmonics
-2-1.5
-1-0.5
00.5
11.5
2
0 2 4 6 8 10 12 14
Phase (radian)
Am
plitu
de (n
orm
aliz
ed)
26
Conductor Utilization In PortionIL=0.5 δ IW =0.5 δ
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)
KCuz
Portion UtilizationSine Wave, Insulation Penalty
Maximum conductor utilization is achieved with single layer portions, but a large number of portions is required.
12
34
56
7Layers
Sum of 10 Harmonics
-2-1.5
-1-0.5
00.5
11.5
2
0 2 4 6 8 10 12 14
Phase (radian)
Am
plitu
de (n
orm
aliz
ed)
27
Loss Equivalent Portion ThicknessIL=0.0 δ IW =0.0 δ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)
Equi
vale
nt T
hick
ness
(in
skin
dep
ths)
1
2
34
56
7
Layers
Loss Equivalent ThicknessSine Wave, No Insulation
Sum of 10 Harmonics
-2-1.5
-1-0.5
00.5
11.5
2
0 2 4 6 8 10 12 14
Phase (radian)
Am
plitu
de (n
orm
aliz
ed)
28
2 * Ip
Ip
Amplitude
radian
Ip
2 * Ip
)sin()cos()( tnnbtnnan
tf
Fourier Decomposition Of Theoretical Waveshapes
2/DC 2/DC- DC/2)-(1
2
... 5, 3, 1,
DC)2
sin(DC
80
22
n
nn
Ipb
a
n
n
... 5, 3, 1,0
DC)2
sin(4
nb
nnIpa
n
n
29
)sin()cos()( tnnbtnnan
tf
Fourier Decomposition Of Theoretical Waveshapes
DCDC- DC)-(2
2
... 3, 2, 1,
DC) sin( DC)-(1 DC
20
22
n
nn
Ipb
a
n
n
... 3, 2, 1,0
DC) sin(2
nb
nnIpa
n
n
2 * Ip
Ip * (1- DC)
Amplitude
radian
Ip
- Ip * (DC)
Ip
30
Loss Equivalent Portion ThicknessIL=0.0 δ IW =0.0 δ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)
Equi
vale
nt T
hick
ness
(in
skin
dep
ths)
1
2
3
4
5
6
7 Layers
Loss Equivalent ThicknessComplex Wave, No Insulation
Sum of 10 Harmonics
-2
-1.5
-1
-0.50
0.5
1
1.5
2
0 2 4 6 8
Phase (radian)
Am
plitu
de (n
orm
aliz
ed)
31
Loss Equivalent Portion ThicknessIL=0.0 δ IW =0.0 δ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)
Equi
vale
nt T
hick
ness
(in
skin
dep
ths)
1
2
3
4
5
6
7 Layers
Loss Equivalent ThicknessComplex Wave, No Insulation
Sum of 10 Harmonics
-2
0
2
0 2 4 6 8
Phase
Am
plitu
de
32
Core Loss Introduction
33
Magnetic Material
• One Oersted is the value of applied field strength which causes precisely one Gauss in free space.
• Permeability is the relative gain in magnetic induction provided by magnetic material.
• Magnetic Material consists of matter spontaneously magnetized.– Magnetic Material in demagnetized state is
divided into smaller regions called domains.– Each domain spontaneously magnetized to
saturation level. – Directions of magnetization are distributed so
there is no net magnetization.– Crystal anisotropy and stress anisotropy
create preferential orientation of spontaneous magnetization within each domain.
– Magnetostatic energy is associated with induced monopoles on surface.
– Exchange energy resides in domain wall as a result of nonparallel adjacent atomic spin vectors.
– Domain structure evolves to achieve relative local minimum of total stored energy.
Iex
Φ
34
Magnetization Microscopic Effects
• Soft magnetic material provides increased magnetic induction from induced alignment of dipoles in domain structure.
• Magnetization process converts material to single domain state magnetized in same direction as applied field.
• Magnetization process involves domain wall motion then domain magnetization rotation.
• Low frequency magnetization characteristics for magnetic material display energy storage and dissipation effects.
• Material voids and inclusions =>irreversible magnetization (Br, Hc)
B
H
Hc
Br
35
Optimal Transformer Turns
36
Maximum J
CustomerLimit
MaximumWinding
Loss
ElectricalRequirements
(regulation,efficiency)
MaximumTemperature
Rise
Design Considerations AffectingCurrent Density: J
)( 2JLossCoil Considering insulation and eddy current penalties
37
)( BLossCore
Design Considerations AffectingFlux Density: ΔB
Maximum B
BpeakTransient
OCLLinearity
MaximumCore Loss
BpeakSteady State
ElectricalRequirements
(efficiency)
MaximumTemperature
Rise
Saturation
Where exponent β is determined through empirical core loss testing
38
• For given core and winding regions, J and ΔB function in a competing relationship.– Decreasing ΔB is equivalent to increasing turns of all
windings by the same proportion.– Increasing turns of all windings by a given proportion
generates proportionately higher current density.• For a linear transformer, selection of turns on any one
winding, uniquely determines J and ΔB densities and therefore total loss for a specific application.
J
ΔB
Selection Of Transformer Parameters: J , ΔB , KCu , KFe
39
p
corepcoil N
FNFr losstransformeTotal 2
• For given conductor and core regions, the normalized expression for low frequency winding loss can be extended and combined with an empirically derived core loss result to yield:
• Fcoil and Fcore relate exponential functions of primary turns (Np) to coil and core losses respectively.
• n is the empirically derived exponential variation of core loss with magnetic flux density.
• Without a constraint of core saturation, minimum transformer loss is achieved with primary turns:
implying =>
Selection Of Transformer Parameters
22
coil
corep F
FN
Insulation and eddy current impacts
2
LossWinding
LossCore
Empirical tests characterize core material in application conditions
40
2
sec
2
2
sec
sec
2
pp
windowCucoil
pp
pwindowCu
pp
pi
i
ii
VVAI
AKyF
NV
VAIAK
yLossCoil
NV
VAINI
NILossCoilFrequencyLow
Determination Of Fcoil
Reflects insulation and eddy current loss penalties
41
Determination Of Fcore
core
pcoreFecore
pcore
pcoreFe
coreFe
corep
p
fA
VKKVolumeFand
NfA
VKKVolumeCore Lossthen
BKVolumeLossCoreIf
AfN
VKB
0
0
0
1
,
Reflects empirical characterization of core loss for specific operating conditions and environment
42
Empirical Test: Verify
43
Φ
IsIp
leakageΦ leakageΦ
Transformer Realities
Winding loss
Leakage magnetic flux
Core Loss and Magnetic Energy applied to excite core
44
Coupled Coils
vp(t)
ip(t)
+
-Lp
is(t)
Ls
M , k
RL
+
-vs(t)
Zi
k is coupling coefficientM is mutual inductance
dtdiM
dtdi
L sppp v
dtdiL
dtdi
M ss
ps v
45
Finding k and M Empirically
spLLkM
shortedsecondary with sc inductanceprimary L re whe1 p
sc
LLk
vp(t)
ip(t)
+
-Lp
is(t)
Ls
46
vp(t)
ip(t)
+
-Lp
is(t)
Ls
M , k
RL
+
-vs(t)
Zi
Leakage Inductance
• Leakage inductance represented if Qp <<1
s
L
LR
pQ where Q1
)1()(p
2s
j
kLjRLL
jZ L
s
pi
47
Lumped Series Equivalent Test Method
Primary Lp Ls
Rp Rs
Secondary
ss
pp
p
ss
RLL
kR
)Lk(
RLIf
2
2
Resistance EquivalentPrimary
1Inductance Leakage EquivalentPrimary
,
48
Empirical Shorted Load Test
ip(t)
+
-Lp
is(t)
Zi
n
nfIn )(
n n
n n
nfIergyAverage EnMeasuredEnergyAverage
nfILossWindingMeasuredLossWindingAC
)]([
)]([
LossDC Winding LossAC WindingCoil Loss
49
Core Loss Test Method Challenges
• Core magnetization is nonlinear process with nonlinear loss effects so Fourier Decomposition may be problematic
• Application waveshapes are difficult to generate– Rectangular voltage– Triangular current– Commercial impedance test equipment is
based on sinusoidal testing at low amplitude• Accurate loss measurement for complex
waveshapes is challenging
50
Sine Voltage Loss Measurement Challenge
Measured Loss Error from Uncompensated Phase Shift vs Inductor Q
Sine Wave
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120
Q
Pow
er M
easu
rem
ent E
rror
Mul
tiplie
r (x
% p
hase
err
or)
Q of 100 causes power measurem
ent
error ~158x phase error
51
Empirical Open Load Testir(t)
+
-Lp
ip(t)
ZiParallel resonant capacitor
facilitates accurate loss
measurem
ent
52
Rectangular Voltage Loss Measurement Challenge
Rectangular Voltage Loss MeasurementPotential Time Delay
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (Period)
Nor
mal
ized
Am
plitu
de
VoltageCurrent
Loss Impact
Time Delay
53
Rectangular Voltage Loss Measurement Challenge
Loss Measurement Error vs Uncompensated Time Delay0.5 Duty Cycle (Q ~ 31.83)
-100
-80
-60
-40
-20
0
20
40
60
80
100
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Time Delay (% of Period)
Loss
Mea
sure
men
t Err
or (%
)
Rectangular Voltage Loss MeasurementPotential Time Delay
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (Period)
Nor
mal
ized
Am
plitu
de
VoltageCurrent
Time Delay0.05% period time delay causes
20% loss measurement error
54
Normalized Rectangular Wave Loss vs Duty Cyclecalculated from fixed core loss resistance
(α=β=2)
0
1
2
3
4
5
6
7
8
9
10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Duty Cycle
Nor
mal
ized
Los
s Fixed VoltageFixed ET
Linear System AssumptionIllustrates Loss Variation(Function of Duty Cycle)
Duty CycleIncrease
Reverse Voltage
Increase
Fixed ET
Nonlinear loss variation
despite linear system
v(t)
+
-
i(t)
LR
55
Modified Core Loss Estimation
56
Notions for Modified Core Loss Calculation Method
• Characterize a given piecewise flux excursion using a sinusoidal equivalent derivative which provides same peak flux and average slope over the interval
• The resultant induced loss by this sinusoidal equivalent derivative will be weighted by the effective duty cycle of the induced loss
• Leverage benefits of sinusoidal empirical test methods
• Facilitate consistent and application relevant transformer core loss test results– Correct peak flux density– Consistent piecewise flux
derivative
[1]
Sinusoidal Equivalent DerivativeSED
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Time (Period)
Nor
mal
ized
Am
plitu
de
Sinusoidal Equivalent DerivativeSEDLinear Flux Trajectory
57
Further Loss Weighting
If instantaneous loss is presumed to vary with the power of the flux derivative [1]:
then a further weighting factor can be determined to scale the measured sinusoidal loss
Note that for an exponent greater than 1, sine wave voltage generated loss is greater than square wave voltage generated loss as demonstrated historically
dtdBtP densityflux peak fixed)(
Ratio of Sine Wave Loss to Square Wave Loss vs Alpha α
calorimetric
calorimetric
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1 1.2 1.4 1.6 1.8 2 2.2 2.4
Alpha α
Nor
mal
ized
Rat
io
58
Compare Three Core Loss Estimation Methods
• iGSE– Improved Generalized Steinmetz Equation [1]
• FHD – Fourier Harmonic Decomposition
• SED– Sinusoidal Equivalent Derivative
Initial comparisons will be based on Steinmetz power law representation as established for specific domains of sinusoidal excitation.
59
Comparison of Core Loss Calculation MethodsTriangular Flux ShapeFixed Equivalent Core Loss Resistanceα=β=2
Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=β=2)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=β=2)
0
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Methods consistently calculate loss for linear system
Duty CycleDuty Cycle
Duty Cycle = 1.0 Duty Cycle = 1.0
60
Comparison of Core Loss Calculation Methods Triangular Flux ShapeEddy Current Shielded Laminationα=1.5 , β=2
Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=1.5 β=2)
0
0.5
1
1.5
2
2.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=1.5 β=2)
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Derivative Based Methods Underestimate
Flux Crowding Impacts
Duty CycleDuty Cycle
Duty Cycle = 1.0Duty Cycle = 1.0
61
Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=1.71 β=1.95)
0
0.5
1
1.5
2
2.5
3
3.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=1.71 β=1.95)
0
1
2
3
4
5
6
7
8
9
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Comparison of Core Loss Calculation MethodsTriangular Flux Shape 0.001 Permalloy 80 α=1.71 , β=1.96
Duty CycleDuty Cycle
Duty Cycle = 1.0Duty Cycle = 1.0
Potential Flux Crowding Im
pact
62
Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=1.5 β=2.6)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)
(α=1.5 β=2.6)
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle
Nor
mal
ized
Los
s
iGSE
FHD
SED
Comparison of Core Loss Calculation MethodsTriangular Flux Shape 3C85 Ferriteα=1.5 , β=2.6
Duty Cycle
Duty Cycle = 1.0
FHD underestimates ferrite triangular loss
Duty Cycle
Duty Cycle = 1.0
63
Calculated Normalized Harmonic Loss: FHD
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7 8 9 10
Harmonic Order
Nor
mal
izee
d to
Tot
alHarmonic Decomposition Problemα=1.5 , β=2.6
Sum of 10 Harmonics
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 2 4 6 8 10 12 14
Phase (radian)
Ampl
itude
(nor
mal
ized
)
Sum of 1 Harmonic
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 2 4 6 8 10 12 14
Phase (radian)
Ampl
itude
(nor
mal
ized
)
Presumed Significant Waveshapingwith Minimal Incremental Loss
64
Observations of Loss Methods• iGSE and SED deliver consistent loss estimates from
Steinmetz parameters since both methods presume instantaneous loss to be proportional to the power of the flux derivative
• SED facilitates meaningful empirical test implementation beyond mathematical application of Steinmetz equation:– Evaluates core capacity for application driven flux
density– Generates application rated average winding voltages– Generates rated instantaneous loss over flux excursion
interval– Facilitates resonant test methods for accurate and
consistent results in production environment
65
Evaluate Loss using Harmonic Coil Loss Analysis and SED Core Loss Estimating Method
66
Sum of 10 Harmonics
-0.5
0
0.5
1
1.5
2
0 2 4 6 8 10 12 14
Phase (radian)
Am
plitu
de (n
orm
aliz
ed)
Example Of Coil Harmonic Loss Testing
Total
Radian
168 W Forward Transformer 300 kHz3 Watt Maximum Winding Dissipation
Losses By Harmonic: 16 V in
0.0
0.5
1.0
1.5
2.0
2.5
3.0
DC 2 4 6 8 10Harmonic Order
Loss
(Wat
t)
Calculated
Actual (5 harmonics)
Losses By LayerTabtronics: 568-6078, 16 V in,
53% Duty Cycle
0.00.10.20.3
0.40.50.6
1 2 3 4 5 6 7
Layer Number
Loss
(Wat
t)
ACDC
67
Loss Summary168 W Forward Converter
DC
Coil
AC
Coil
AC
Core
Total
00.5
11.5
22.5
33.5
Loss Summary
Po
we
r L
oss (
W)
8 V, 21 A, 300 kHz
68
Other Observed Core Loss Factors
• Fundamental variables (peak field density, frequency, temperature)
• Biased operating application waveshape [2]• Flux density relaxation during circuit commutation
intervals• Flux crowding from eddy current shielding• Designed air gap => fringing effects• Nonuniform core cross sections => nonuniform
magnetic field densities => nonuniform loss density• Unintended micro-crack(s)• Mechanical Stress (magnetic anisotropy)• Irregular or mismatched core segment interfaces• Material manufacturing lot variances (unintended
substitutions !)
69
Core Loss Experiences
Transformer Loss (PSFB, 214W, 100 kHz)
Core Loss
Core Loss
Core Loss
Core Loss
Coil Loss
Coil Loss
Coil Loss
Coil Loss
0
1
2
3
4
5
6
7
20˚C 100˚C 100˚C Coated Type A 100˚C Coated Type D
Condition
Pow
er (W
atts
)
EFD20/10/7
Table 1: expected performance comparison on ungapped core set
Material NLP Terminals (4-5) 350Vrms @ 200kHz
20˚C
NLP Terminals (4-5) 350Vrms @ 200kHz
100˚C 3C94 1.92W 1.022W 3C96 2.05W 0.74W
(3C96 - 3C94) 0.13W -0.282W
Micro-cracks – Misalignment
>3x core loss increase
70
Summary
71
Recommendations
• Rigorously measure performance of magnetic components used in demanding applications prior to commencing production.– Use application relevant high frequency and high
amplitude test methods to ensure consistent application results throughout production.
• If the magnetics have significant impact on the end system’s market differentiation then a collaborative Design Partnership between power system developer and transformer developer will maximize the custom magnetics’ utility for the end system.– Capable and trustworthy design partners with
effective project management is necessary.
72
References
[1] J. Li,T. Abdallah, and C. R. Sullivan, “Improved calculation of core loss with nonsinusoidalwaveforms,” in Industry Applications Conference, 36th IEEE IAS Annual Meeting, vol. 4, pp. 2203-2210, 2001.
[2] J. Muhlethaler, J. Biela, J. W. Kolar, and A. Ecklebe, “Core losses under DC bias condition based on Steinmetz parameters,” in Proc. of the IEEE/IEEJ International Power Electronics Conference (ECCE Asia), pp. 2430–2437, 2010.
73
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